Signed by scout Jose Serra, Alburquerque began his professional career in 2006 with the AZL Cubs, in the Chicago Cubsfarm system. He went 0–2 with a 5.98 ERA in eight games (five starts) that season. He also had 15 strikeouts in 12⅔ innings. In 2007, he played for the Boise Hawks and Peoria Chiefs, going a combined 4–6 with a 5.83 ERA in 21 games (10 starts). In 66⅓ innings, he struck out 69 batters. He did not play at all in 2008.

Alburqueque began the 2009 season in the Cubs system, pitching for the Daytona Cubs. However, he was traded to the Colorado Rockies partway through the season as a player to be named later in a deal that sent Jeff Baker to the Cubs.[1] He finished the season with the Tulsa Drillers. Overall, he went 2–3 with a 2.80 ERA in 47 relief appearances, striking out 75 batters in 61 innings. He pitched for the Oilers again in 2010, going 2–4 with a 4.98 ERA in 25 relief appearances.[2]

Following the 2010 season, he became a free agent and signed a minor league contract with the Detroit Tigers.